that at least one pair of samples differs. Let’s say you are interested in treatments A, B and C in an experiment, and will conduct hypothesis tests for differences between A and B, A and C, and B and C, each with a significance level of alpha = 0.05.
Each time you do an independent test, the individual Type I error is 0.05, so the probability of not making an error is 0.95. The probability of not making such an error on three consecutive tests is 0.95 * 0.95 * 0.95 = 0.8574. So the Type I error rate overall, or the familywise error rate, is 10.8574 = 0.1426. This is considerably more than the individual rate, and it increases as the number of comparisons increase.
If a is the probability of individual comparisonwise type I error, then the probability a_{FW} of familywise type I error is usually calculated as follows:

where C is the total number of individual comparisons made. You can see that to keep the overall familywise error rate at 0.05 you will need to substantially reduce the alpha level for each test.